CLASS 10 IMO WORKBOOK

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(1)10. 5. (2007-2011). INSTANT.

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(7) IIT-JEE | AIEEE | NEET | BOARDS | OLYMPIAD | NTSE. FOUNDATION COURSE For Classes 8, 9 & 10 Class 8. Class 9. Class 10.

(8) 1st. Year 2007.

(9) Class 10 . 1st IMOSETA - 2007. 2 . SECTION I : LOGICAL REASONING Direction (Q1 3): In each of the following three questions a series of numbers/alphabets is given which follows certain rules. One of the numbers/alphabets is missing. Choose the missing number/ alphabets from the alternatives given below. 1. . 284, 140, 68, ? (A) 70 . (B) 34 . (C) 32 . (D) 60 . (B) 18 . (C) 24 . (D) 22 . (B) ETK . (C) ERS . (D) ERJ . (E) None of these. 2. . 17496, 1944, 216, ? (A) 20 (E) None of these. . 3. . AXB, BWD, CVF, DUH, ? (A) ETJ (E) None of these. Direction (Q4 5): In each of the following questions there are five groups of letters four of them are alike in some manner, while one is different. Find out the different one. . 4. . (A) NOPR . (B) SURT . (C) PROQ . (D) FHEG . (B) BDFH . (C) IKMO . (D) YACE . (E) None of these. 5. . (A) ACEG (E) None of these. . 6. . In a row of 40 children facing North, Satish is eighth to the right of Ajay. If Ajay is 18th from the right end of the row, how far is Satish from the left end of the row? (A) 32nd . (B) 10th . (C) 31st . (D) 29th . (E) None of these. 7. . In the following figure, the represents educated, the represents urban and the the honest people. Study the figure carefully and answer the question which follow. . represents s . 1 3 6 4 . 7 2 5 . Which number represents who are honest but not educated and not urban? (A) 2 . (B) 1 . (C) 6 . (D) 3 . (E) None of these. 8. . In a certain code ‘PURE’ is written as ‘QVQD’ and ‘COPE’ is written as ‘DPOD’. How is ‘WHEN’ written in that code? (A) XIFO (E) None of these.. (B) VGDM . (C) XIDM . (D) VGFO .

(10) SETA 9. . 1st IMO - 2007 Class 10 . 3 . Arrange the words in the sequence in which they occur in dictionary. 1. . Indorse . (A) 1 2 3 4 . 2. . Infant . 3. . (B) 1 2 4 3 . Infidel . (C) 4 3 2 1 . 4. . Inflect . (D) 3 4 2 1 . (E) None of these. Direction (Q10 11): In the following questions select from the answer choices an appropriate number to replace the question mark 3 . 10. . 6 . 45 . (A) 117 . 9 . 11 1 . 85 . ? . (B) 122 . 2 . (C) 123 . (D) 141 . (E) None of these. . 9 . 6 99 . 11. ? . (A) 10 . (B) 14 . 15 . (C) 5 . (D) 9 . (E) None of these. 12. Seema and Rajat start together from a point. They walk 10 kms towards North. Seema turns to her left and walk 5 kms, while Rajat turns Right and walk only 3 kms. Now Seema turns towards her left and Rajat towards his right and both walk 15 kms forward. How far are they from each other (A) 2 kms . (B) 8 kms . (C) 13 kms . (D) 15 kms . (E) None of these. 13. How many right angled triangles are there in the given figure (A) 12 . (B) 15 . (C) 9 . (D) 11 . (E) None of these. 14. Assume A = 0, B = 2, C = 1, D = 3, E = 4, F = –2, M = 10 B × C + A + D × M = ? (A) 32 . (B) 52 . (C) 22 . (D) 42 . (E) None of these. 15. Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group? (A) March . (B) January . (C) July . (D) June . (E) May. 16. If P denotes +, Q denotes –, R denotes × and S denotes ¸ , which of the following statements is correct. Select the appropriate number among the given choices. 36 R 4 S 8 Q 7 P 4 = ? (A) 58 (E) None of these.. (B) 55 . (C) 63 . (D) 15 .

(11) Class 10 . 1st IMOSETA - 2007. 4 . 17. The positions of how many digits in the number 7354612 will remain unchanged after the digits within the number are rearranged in descending order from left to right? (A) One . (B) Two . (C) Three . (D) More than three. . (E) None of these. 18. X and Y are sisters. Y is wife of Z, P is son of Q, M is daughter of Y. N is husband of X, Q is father of Y. O is daughter of L, K is wife of L. X is mother of L. Who is the brother of L? (A) M . (B) Z . (C) L . (D) Q . (E) P. Direction (Q19 20): Read carefully the information given below. In a group of five boys A, B, C, D and E. A and C are good in English and Maths, B and C are good in English and General knowledge, E and D are good in Science and Drawing. B and D are good in Drawing and General knowledge. While E is good in Drawing, Maths and Science. 19. Who is good in English, Drawing and General knowledge? (A) A . (B) B . (C) E . (D) C . (E) D. 20. Who is good in English and Maths but weak in General kowledge? (A) E . (B) C . (C) A . (D) D . (E) B. . SECTION II : MATHEMATICAL REASONING 21. The weighted median A w is equal to (A). å wx å w . (B). å xF å F . (C). å. x n . (D). å x . (E) None of these. 22. What will be the difference of the roots of quadratic equation 4y 2 – 4y + 1 = 0? (A) 0 . (B) 1 . (C) -. 1 2. (D) 2 . (E) None of these. 23. The area of sector is equal to (A) pr 2 . (B) . pr 2 q 360 °. (C) p(R + r) (R – r) . (D) 2pr . (E) None of these. 24. The mode of data given below is 16. What is the value of x ? 13, 15, 16, 14, 16, 14, 13, 14, 13, x, 16, 17, 18, 17 (A) 15 . (B) 16 . (C) 17 . (D) 18 . (C) 6 . (D) 8 . (E) None of these. 25. The number of subsets of A = {0, 7, 8} will be (A) 3 (E) None of these.. (B) 5 .

(12) SETA . 1st IMO - 2007 Class 10 . 5 . 26. If a, b be the roots of equation 4x 2 – 7x + 3 = 0 then the value of 25 12 (E) None of these. (A) . (B) . 23 8 . (C) . a b + will be b a. 24 25 . (D) . 24 23 . 27. If the price of a material is increased by 10% and again increased price is decreased by 10%, then what will be the loss percentage? (A) 1% . (B) 1.5% . (C) 2% . (D) 5% . (E) None of these. 28. Which of the statements given below is correct, if discriminant for equation 5x 2 – 4x + 2 = 0 is D ? (A) D > 0 . (B) D = 0 . (C) D < 0 . (D) D is not defined . (E) None of these. 29. If p is 25% less than q, then q is x% more than p, where x = ? 1 (A) 33 % 3 . (B) 25 . 2 (D) 16 % 3 . 1 (C) 33 3 . (E) None of these. 30. The selling price of two materials is Rs. 500. If there is loss of 20% on the first material and profit of 20% on the other material, then what will be the total percentage loss? (A) 4% . (B) 2.5% . (C) 3% . (D) 3.5% . (E) None of these. 31. The curved surface area of cone is equal to (A) prl square unit . (B) . 1 2 pr h cubic unit 3 . (C) pr(l + r) square unit (D) pr 2 l cubic unit . (E) None of these. 32. The volume of spherical shell is equal to 4 p(R 3 - r 3 ) 3 (E) None of these. (A) . (B) 4pr 2 . (C) p(R + r) (R – r) . (D). 4 3 pr 3 . 33. The legs of a right angled triangle are 8 cm and 15 cm. The radius of the circle inscribed in the triangle is (in cm) 15 cm . (A) 1 . (B) 2 . (C) 3 . (D) 4 8 cm . (E) None of these. 34. If x – k divides x 3 – 6x 2 + 11x – 6 =0, then k can't be equal to (A) 1 . (B) 2 . (C) 3 . (D) 4 . (E) None of these. 35. The system of equations tx + ty + t = 0 and x + (2 – t)y = 2 has no solution, if t = (A) 2 (E) None of these.. (B) 1 . (C) – 6 . (D) 4 .

(13) Class 10 . 1st IMOSETA - 2007. 6 . 36. In the given diagram shown below, if PB = 8 cm, AB = 4 cm, PD = 6 cm, then CD = ? . A . 4 cm . C 16 cm 3 (E) None of these. (A) . x 2 - 2 4 x + 1 = 0 . ? . (B) 10 cm . 37. If one root of a quadratic equation is (A). B . (B). D . 8 cm . P . 6 cm. (C) 6 cm . (D) 7 cm . 1 , then the quadratic equation can be 4 - 3 . x 2 - 4 x + 1 = 0 . (C). (D). x 2 + 2 4 x + 1 = 0 . x 2 - 2 3 x + 1 = 0 . (E) None of these. 38. If base of a right angled triangle is twice the base of another right angletriangle and height of first right angle triangle is 1/4 th of other's height then what will be ratio of area of triangle one to triangle two. (A) 1 : 1 . (B) 2 : 1 . (C) 1 : 2 . (D) 3 : 2 . (E) None of these. 39. The measure of each exterior angle of a regular pentagon is (A). p radian 6 . (B). 2 p radian 5 . (C). p radian 3 . (D). 3 p radian 5 . (E) None of these. 40. a 2 – b 2 will be a perfect square if the ratio of a and b is (A) 1 : 2 . (B) 3 : 4 . (C) 5 : 4 . (D) 4 : 5 . (E) None of these. . SECTION III : EVERYDAY MATHEMATICS 41. There are three circles each of radius 7 cm. A triangle is formed by joining their centres. The angles at the centre made by the triangle are shown in the given figure, [42°,58°, 80°]. The area of the shaded portion is (A) 11 cm 2 11 2 cm 7 (E) None of these. . (C) . 58° . 22 2 cm (B) 7 (D) . 80° . 4 2 cm 7 . 42. ABCD is a square, inscribed in a circle of radius 14 cm. E, F, G, H are the middle points of the sides DA, AB,BC and CD respectively. The area of the square EFGH will be (A) 89 cm 2 . (B) 196 cm 2 . (C) 98 cm 2 . (D) 392 cm 2 . (E) None of these.. 42° . A . F . E D . B G . H . C .

(14) SETA . 1st IMO - 2007 Class 10 . 7 . 43. Two circular wheels of the same radius r have their central hubs at a distance of a from one another. The minimum length of a fan belt which will pass around both the wheels, is (A) 2(a + pr ) (D) . a - pr 2. (B) . a + pr 2. r . (C) 2a + pr . (E) None of these. . 44. In the figure, ABCD is a square with side 10. BAD is an arc of a circle with centre C. BCD is an arc of a circle with centre A. What is the area of the shaded region? (A) 100 50p. (B) 100 25p. (C) 50p 100 . (D) 25p 100 . (E) None of these. . A . B . D . C . 45. Three men, four women and six children can complete a work in 7 days. A women does double the work a man does and a child does half the work a man does. How many women can complete this work in 7 days? (A) 8 . (B) 7 . (C) 12 . (D) Cannot be determined . (E) None of these. 46. A and B run a kilometre and A wins by 25 sec. A and C run a kilometre and A wins by 275 m. B and C run the same distance and B wins by 30 sec. The time taken by A to run a kilometre is (A) 2 min 25 sec . (B) 2 min 50 sec . (C) 3 min 20 sec . (D) 3 min 30 sec . (E) None of these. 47. Plane A takes off at 4 pm and flies at a constant speed of X mphr. Plane B takes off at 5. 30 pm and flies the same route as that of A at a constant speed of Y mphr. Assuming Y is greater than X. How many hours after 5.30 pm will the plane B overtake plane A? 3 X hr 2 (E) None of these. (A) . (B) . 3 hr 2Y . 3 (C) 2(Y X) hr . 3 X (D) 2(Y X) hr . 48. A sells a bicycle to B at a profit of 20% , B sells it to C at a profit of 25%. If C pays Rs. 225 for it, the cost price of bicycle for A, is (A) Rs. 110 . (B) Rs. 125 . (C) Rs. 120 . (D) Rs. 150 . (E) None of these. 49. 180 oranges are distributed among 70 boys and girls such that each boy get 2 and each girl 3 oranges. The number of boys are (A) 70 . (B) 25 . (C) 30 . (D) 40 . (E) None of these. 50. Twenty litres of a mixture contains milk and water in the ratio of 5 : 3. If four litres of this mixture is replaced by four litres of milk, then the ratio of the milk to that of the water in the container will be (A) 5 : 3 (E) None of these.. (B) 4 : 3 . (C) 7 : 3 . (D) 2 : 3 .

(15) 2nd. Year 2008.

(16) Class 10 . 2nd IMO - 2008. 2 . SECTION I : LOGICAL REASONING 1. . If '+' means '¸', '¸' means '×', '×' means '–' and '–' means '+', what will be the value of the following expression ? 15 ¸ 5 × 9 + 3 – 6 (A) 78 . 2. . (B) 72 . (D) . 30 . (E) None of these. . The positions of how many digits in the number 4231576 will remain unchanged after the digits within the number are arranged in ascending order ? (A) None . 3. . (C) 28 . (B) One . (C) Two . (D) Three . (E) More than three. . If the same functions are applied to reach the results in each of the three sets of numbers, find what number should replace the ? in the last set: 21 . 5 . 28 13 30 . ? . 7 . 25 7 . 10 8 . 24 17 . (A) 30 . 16 2 . (B) 36 . (C) 32 . (D) 35 . (E) 25 . Directions (Q.4 and 5) : Which one of the five answer figures should come after the problem figures, if the sequence were continued? × × . × . × . × × . D. 1 . Problem figures . × . D . × . × . 4. . . Answer figures 2 . (A) 1 . 3 . 4 . (B) 2 . 5 . (C) 3 . 5. . (D) 4 . (E) 5 . Problem figures . Answer figures 1 . (A) 1 . 2 . 3 . (B) 2 . 4 . 5 . (C) 3 . (D) 4 . (E) 5.

(17) Class 10 6. . What should come in place of the question mark in the following number series ? 6 (A) 1045 . 7. . 16 . (B) 941 . 51 208 . ? . 6276 . (C) 836 . (D) 1254 . (E) None of these. . (B) 5189 . (C) 5289 . (D) 5429 . (E) None of these. . Without using any coins, can you determine below how many revolutions a coin will complete if it is rolled around another coin ? The coins are of same size. (A) 1 . 9. . 7 . In a certain code 'GEAR' is written as '5914' and 'ROUTE' is written as '47289'. How is 'GATE' written in that code ? (A) 5187 . 8. . 2nd IMO - 2008. 3 . (B) 2 . (C) 3 . (D) 5 . (E) 6 . The largest box of shoes contains 459 pieces. The next size box contains 153 pieces. They also sell a box with 51 pieces and one smaller sized box. Based on this pattern, how many pieces are in the smaller sized box ? (A) . 15 . (B) 37 . (C) 27 . (D) . 17 . (E) None of these. . 10. Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ? (A) 35 . (B) 28 . (C) 56 . (D) 42 . 11. What is the first term in the exponential sequence below? {_, __, __, 81, 243, 729, ...... } (A) 1 (B) 3 (C) 9 (D) 27 . (E) 49 . (E) None of these. . 12. If A : B = 2 : 3, B : C = 2 : 4 and C : D = 2 : 5, then A : D is equal to (A) 2 : 15 . (B) 2 : 5 . (C) 1 : 5 . (D) 3 : 5 . (E) None of these. . 13. If Blue is called Red, Red is called Black, Black is called White, White is called Yellow, Yellow is called Green and Green is called Orange, then what is the colour of turmeric powder ? (A) Black . (B) White . (C) Green . (D) Yellow . (E) None of these. . 14. Which of the following distances is the longest ? (A) 2 kilometers (B) 500 centimeters (C) 2,300 meters (E) None of these. . (D) 25,000 millimeters . 15. Onefourth of sixty percent of a number is equal to twofifths of twenty percent of another number. What is the respective ratio of the first number to the second number ? (A) 4 : 7 (B) 8 : 13 (E) None of these. . (C) 5 : 9 . (D) Cannot be determined . 16. Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ? (A) Cabbage (B) Brinjal (C) Sweet Gourd (D) Pumpkin (E) Bitter Gourd. 17. Southland Cellular Phone Company offers two different rate plans. PlanA : Rs 45 per month, plus Rs 0.15 per minute of calling time PlanB : Rs 25 per month, plus Rs 0.25 per minute of calling time For how many minutes of calling time do the plans cost the same amount ? (A) 50 minutes (B) 120 minutes (C) 175 minutes (D) 200 minutes (E) None of these..

(18) Class 10 . 2nd IMO - 2008. 4 . 18. Tree is to ground as chimney is to ? (A) Smoke . (B) Sky . (C) House . (D) Garage . (E) None of these. . 19. Jack is taller than Paul, and Bill is shorter than Jack. Which of the following statements would be most accurate? (A) Bill is taller than Paul . (B) Bill is shorter than Paul . (C) Bill is as tall as Paul . (D) It is impossible to tell whether Bill or Paul is taller. . (E) None of these. . is to . 20. . (A) . (B) . as . is to . (C) . (D) . (E) None of these. . SECTION II : MATHEMATICAL REASONING 21. If HCF of 65 and 117 is expressed in the form of 65m + 117n, then the value of m and n respectively is (A) 3, 2 . (B) 3, –1 . (C) 2, –1 . (D) 2, –3 . (E) None of these. . 22. If a and b are the zeros of the quadratic polynomial f(x) = x 2 – x –2, which of the following is the polynomial whose zeros are 2a + 1 and 2b + 1 ? (A) k(x 2 – 4x – 5) . (B) k(x 2 + 4x – 5) . (C) k(x 2 – 5x + 4) . (D) k(x 2 – 2x – 3) . (E) None of these. . 23. What is the value of a and b for which the following system of linear equations has infinite number of solutions ? 2x – 3y = 7, (A) a = – 5, b = – 2 . (a + b)x – (a + b – 3) y = 4a + b . (B) a = 5, b = – 1 . (C) a = – 3, b = – 2 . (D) a = – 5, b = – 1 . (E) None of these. 24. A swimming pool is filled with three pipes with uniform flow. The first two pipes operating simultaneously, fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool five hours faster than the first pipe and four hours slower than third pipe. What is the time required by third pipe to fill the pool ? (A) 6 hrs. . (B) 10 hrs. . (C) 15 hrs. . (D) 18 hrs. . (E) 12 hrs. . 25. A man borrows Rs 1000 and agrees to repay with a total interest of Rs 140 in 12 installments, each installment being less than the preceding by Rs.10. What should be his first installment ? (A) Rs. 120 . (B) Rs. 140 . (C) Rs. 150 . (D) Rs. 180 . (E) Rs. 100 . 26. What is the third vertex of a triangle, if two of its vertices are at (–3, 1) and ( 0, – 2) and the centroid is at the origin? (A) (2, 1) . (B) (3, 1) . (C) (3, 2) . (D) (4, 1) . (E) (0, 2) . 27. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double of a red ball, what is the number of blue balls in the bag? (A) 5 . (B) 8 . (C) 10 . (D) 12 . (E) 3.

(19) Class 10 . 2nd IMO - 2008. 5 . 28. The mean of the following frequency table is 50, but the frequencies f 1 and f 2 in class 20–40 and 60–80 are missing. What are the missing frequencies? Class interval 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 Total Frequency. (A) 12, 18 . 17. (B) 20, 24 . ?. 32. ?. (C) 32, 28 . 19. 120 . (D) 28, 24 . (E) None of these. . 29. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If æ 1 ö its volume is ç ÷ è 27 ø (A) 15 cm . th . the volume of cone, the height at which the section is made is . (B) 20 cm . (C) 10 cm . (D) 25 cm . (E) None of these. B . 30. In the given figure, O is the centre, PAQ is tangent, ÐPAB = 58°, then ÐAQB is (A) 58° . (B) 29° . (C) 106° . (D) 26° . O 58° P A . C Q . (E) None of these. 31. In the given figure, P and Q are midpoints of AC and BC, then 5AB 2 = (A) 4(AQ 2 + BP 2 ) . (B) 4(AC 2 + BC 2 ) . (D) 4(PC 2 + CQ 2 ) . (E) None of these. . (C) (AP 2 + BQ 2 ) . (D) can't be said . P C . 32. In a quadrilateral ABCD, AD = BC. If P, Q, R, S are midpoints of AB, AC, CD and BD respectively, then PQRS is a (A) square (B) rectangle (C) rhombus . A . (E) None of these. . B . Q . R . D S A . C Q . P . B . 33. The sum of the series 45 2 – 43 2 + 44 2 – 42 2 + 43 2 – 41 2 + 42 2 – 40 2 + ........ to 30 terms is (A) 2000 (B) 1590 (C) 2143 (D) 2220 (E) None of these. x + 10 -. 6 . = 5 has x + 10 (A) an extraneous root between –5 and –1 (C) two extraneous roots (E) None of these. . 34. The equation. (B) an extraneous root between – 10 and – 6 (D) a real root between 20 and 25 . 35. The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, what is the speed of the aeroplane ? (A) 432.6 kmph . (B) 338.8 kmph . (C) 439.2 kmph . (D) 332.7 kmph . (E) None of these. . 36. If cosec q – sin q = l and sec q – cos q = m, then what is the value of l 2 m 2 (l 2 + m 2 + 3) ? (A) 0 . (B) 1 . (C) 2 . 37. 50 circular plates each of radius 7 cm and thickness . (D) –3 . (E) None of these. . 1 cm are placed one above another to form a 2 . solid right circular cylinder. What is the total surface area of the cylinder so formed ? (A) 1230 cm 2 . (B) 1332 cm 2 . (C) 1408 cm 2 . (D) 1560 cm 2 . (E) None of these..

(20) Class 10 . 2nd IMO - 2008. 6 . 38. PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi–circles are drawn on PQ and QS as shown in the figure. What is the perimeter of the shaded region ? (A) 6p cm . (B) 10p cm . (C) 12p cm . Q . P . R . S . (D) 16p cm . (E) None of these. 39. What annual installment will discharge a debt of Rs. 5445 due 4 years hence, the rate of interest being 14 % p.a. simple interest ? (A) Rs. 1125 . (B) Rs. 1000 . (C) Rs. 1225 . (D) Rs. 1275 . (E) None of these. D . 40. ABCD is a trapezium in which AB | | CD and AB = 2CD. What . C O . is the ratio of the areas of triangles AOB and COD ? (A) 2 :1 . (B) 4 :1 . (C) 3 :1 . (D) 3 : 2 B . A . (E) None of these. . SECTION III : EVERYDAY MATHEMATICS 41. In a soccer tournament the average of goals scored in Anupam’s first 5 games was 6.4. The average of his next four games was 6.5. If there were 9 goals scored in the tenth game what was the overall average ? (A) 7.6 . (B) 6.7 . (C) 9.2 . (D) 4.8 . (E) None of these. . 42. If the numerator of a fraction is increased by 200% and the denominator of the fraction is increased 9 by 150%, the resultant fraction is . What is the original fraction ? 35 (A) . 3 10 . (B) . 2 15 . (C) . 3 16 . (D) . 2 17 . (E) None of these. . 43. Two girls agree to go on a road trip together. They travel (x + 5) km on the first day. On the second day they travel 2 km more than half of the distance they travelled on the first day. On the third day they drove 3 times as far as they did on the second day. If they drove 5000 km total, find the value of x. (A) 1670 . (B) 1659 . (C) 1750 . (D) 1756 . (E) None of these. . 44. The average age of a group of teachers and professors is 40. If the teachers average 35 years and the professors 50 years, then what is the ratio of the number of teachers to professors ? (A) 1 : 2 . (B) 2 : 1 . (C) 5 : 3 . (D) 3 : 5 . (E) None of these. . 45. The lookout on a pirate ship is keeping his eyes open for land. From his perch 6 m above the water he can only look down at a 60 degree angle. He cannot see the land (X) from his position at t = 0 but in 3 seconds it comes into view. What was the distance from the ship’s position at t = 0 to land ? . (A) 13.39 m (B) 15.39 m . 60° 6m . (C) 14.39 m (D) 19.39 m (E) None of these.. 30° A t = 0 . 1 m/s . B . X .

(21) Class 10 . 2nd IMO - 2008. 7 . 46. The distance from an observation point X to a comet at a given time is known to be 3.5 million kilometers. Given that a line drawn from the comet to the observation point is parallel to a line going through the center of the earth, find the values of y. (A) 1.5 million kilometers (B) 1.3 million kilometers (C) 1.7 million kilometers . Comet y X . x . (D) 1.75 million kilometers 60° . (E) None of these. . Earth . 47. Four children are playing with marbles. At the end of the day one child has 4 less than half the marbles, the second child has 6 more than one fifth of the marbles, the third child has one third of what the first child had and the fourth child has 1 less than the third child. How many marbles are there ? (A) 60 . (B) 65 . (C) 50 . (D) 55 . (E) none of these. . 48. Mania and Sania graduated from university together. Sania became a teacher and earned half what Mania earned for 5 years. Mania spent 1/3 of her money; Sania spent 1/4 every year for those 5 years. Sania has Rs. 80,000 after 5 years. How much does Mania have ? (A) Rs. 15333.3 . (B) Rs. 142222.22 . (C) Rs. 15000 . (D) Rs. 152222.52 . (E) None of these. . 49. How many minutes is it until 5:00 if forty minutes ago it was four times as many minutes past 2 o’clock ? (A) 30 mins . (B) 35 mins . (C) 28 mins . (D) 29 mins . (E) None of these. . 50. If a tyre rotates at 150 revolutions/min when the truck is travelling 40 km/h, what is the circumference of the tyre ? (A) 4.44 m . (B) 5 m . (C) 5.44 m . (D) 6 m . SPACE FOR ROUGH WORK. (E) None of these. .

(22) 3rd. Year 2009.

(23) 3rd IMO - 2009. SECTION I : LOGICAL REASONING 1. . In how many ways can you join the two shapes shown here to make a figure with a line of symmetry? (A) 0 . 2. . (B) 320 . (C) 550 . (D) 2560 . (B) put . (C) ta . (D) Can't be determined . (B) Jack . (C) Pawan . (D) Ashish . (B) 30 metres . (C) 60 metres . (D) 40 metres . Choose the venn diagram which best illustrates the three given classes. Citizens, Educated, Men (A) . 8. . (D) 18 . Gaurav walks 20 metres towards North. He then turns left and walks 40 metres. He again turns left and walks 20 metres. Further, he moves 20 metres after turning to the right. How far is he from his original position ? (A) 20 metres . 7. . (C) 20 . Ashish is heavier than Govind. Mohit is lighter than Jack. Pawan is heavier than Jack but lighter than Govind. Who among them is the heaviest ? (A) Govind . 6. . (B) 22 . In a certain code language, 'dom put ta' means 'bring hot food', 'put tir sop' means 'food is good' and 'tak da sop' means 'good bright boy'. Which of the following means 'hot' in that language? (A) dom . 5. . (D) 3 . In the series given below, one term is wrong. Find out the wrong term. 5, 10, 40, 80, 320, 550, 2560 (A) 80 . 4. . (C) 1 . In the given series one term is missing. Choose the correct alternative that will continue the same pattern. 0, 2, 8, 14, (.........), 34 (A) 24 . 3. . (B) 2 . (B) . (C) . (D) . In the given matrix, the characters follow a certain trend, row wise or column wise. Find out this trend and choose the missing character accordingly. 18 24 32 12 14 16 3 ? 4 72 112 128 . (A) 2 9. . (B) 3 . (C) 4 . (D) 5 . The adjoining figure shows the network connecting cities A, B, C, D, E and F. The arrows indicate permissible directions of travel. B . C . A . F D . E . What is the number of distinct paths from A to F ? (A) 9 3 rd IMO | LevelI | Class 10 . (B) 10 . (C) 11 2 . (D) None of these.

(24) 3rd IMO - 2009. 10. How many letters of English alphabet [A to Z ] appear same when looked at in a mirror? (A) 10 . (B) 8 . (C) 11 . (D) 13 . 11. One white square is surrounded by four black squares, two white squares are surrounded by six black squares, three white squares are surrounded by 8 black squares. What is the largest possible number of white squares surrounded by n black squares? (A) . n - 1 2 . (B) . n + 1 2 . (C) n + 2 . (D) 2(n + 1) . 12. Choose the best option to complete the given matrix. . (A) . (B) . (C) . (D) . 13. A normal duck has two legs. A lame duck has one leg. A sitting duck has no legs. Ninetynine ducks have total of one hundred legs. Given that there are half as many sitting ducks as normal ducks and lame ducks put together, find the number of lame ducks. (A) 32 . (B) 33 . (C) 34 . (D) 36 . 14. Choose the waterimage of the Figure (X) from amongst the given alternatives. Fig. (X ) . (A) . (B) . (C) . (D) . 15. In the given figure, ABCD is a square of side 2008 cm. It is divided as shown in the figure into four equal squares. The top right hand side square is again divided into 4 equal squares. Again the top right hand square is divided into four equal squares. A . B O . D . C . The side of each smallest square is _______ (A) 1004 cm . (B) 1002 cm . (C) 502 cm . (D) 251 cm . 16. A plank is placed on a tiled floor. What fraction of the floor is not covered by the plank? . (A) . 1 4 . (B) . 3 8 . (C) . 3 . 17 64 . (D) . 5 8. 3 rd IMO | LevelI | Class 10 .

(25) 3rd IMO - 2009. 17. The following housepatterns were created using match sticks: . House 1 Houses 4 Houses 7 Sticks 5 Sticks 17 Sticks 29 Which one of the numbers given below cannot be the number of sticks used to create a complete row of houses ? (A) 2361 . (B) 2369 . (C) 2309 . (D) 2008 . 18. What should be the number opposite 3? . (A) 1 . 2 1 3 . 3 1 5 . 4 2 3 . (i) . (ii) . (iii) . (B) 6 . (C) 5 . (D) 4 . 19. 8 boxes, all of different sizes, are placed in a row; 2008 books are distributed in such a way that each box receives 2 books more than its next immediate smaller box. How many books does the largest box receive? (A) 258 . (B) 244 . (C) 236 . (D) 264 . 20. The number of prime numbers less than 100, sum of whose digits is 2, is ______ (A) 1 . (B) 2 . (C) 3 . (D) 4 . SECTION II : MATHEMATICAL REASONING 21. If the sum of the number (a ´ 25) 2 and a 3 is divisible by 9, then which of the following is the value for a ? (A) 1 . (B) 7 . (C) 9 . (D) 8 . 22. A pentagon with area 40 has equal sides but not necessarily equal angles. The sum of the five perpendicular distances from a point inside the pentagon to the sides of the pentagon is 16. The side length of the pentagon is ______ (A) . 5 2 . (B) . 5 4 . (C) 12 . (D) 5 . 23. In the figure given below, AG = 6 cm and AB = BC = CD = DE = EF = FG = 1 cm. Semicircles are drawn as shown in the diagram. The total length of the path A to G along the smaller semicircles is x. The length of the path (B to F) along the bigger semicircle is y. Then ______ . A. (A) x < y . B. C. D. (B) x = y . E. F. G . (C) x > y . 24. In the adjoining figure, the parallel lines are marked by arrows. The value of the angle x is ______ (A) 60° . (B) 70° . (C) 80° . (D) 50°. 3 rd IMO | LevelI | Class 10 . 4 . (D) x + y = 6p 80° 70° . x .

(26) 3rd IMO - 2009. 25. In the adjoining figure, AC = 2006 cm, ÐACB = q, BD ^ AC, DE ^ BC, EF ^ AC. Then EF = A D . F q. B . (A) 2006 sin 4q. E . (B) 2006 sin 3q cosq. C . (C) 2006 sin 2qcos 2q. (D) 2006 sinq cos 3q. 26. Four identical coins are placed in a square. For each coin, the ratio of the area to circumference is same as the ratio of circumference to area. Then, find the area of the square that is not covered by the coins. (A) 16(p – 1) . (B) 16(8 – p) . (C) 16(4 – p) . pö æ (D) 16 ç 4 - ÷ 2 è ø. 27. If the roots of the equation x 2 – bx + c = 0 differ by 2, then which of the following is true ? (A) c 2 = 4(c – 1) . (B) b 2 = 4c + 4 . (C) c 2 = b + 4 . (D) b 2 = 4(c + 2) . 28. A pair of fair dice are rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is ______ (A) 0.45 . (B) 0.4 . (C) 0.5 . (D) 0.6 . 29. A rectangle has sides of integer lengths (in cm) and an area of 36 cm 2 . What is the maximum possible perimeter of the rectangle ? (A) 74 cm . (B) 84 cm . (C) 124 cm . (D) 64 cm . 30. Given question has two statements. Statement 1 is Assertion (A) and Statement 2 is Reason (R). Assertion (A) : The measures of the angles of a convex polygon are in arithmetic series. The smallest angle of the polygon is 36°. Reason (R) : Each angle of a convex polygon should be less than or equal to 180°. (A) (A) and (R) both are true and (R) explains (A) (B) (A) and (R) both are true and (R) does not explain (A) (C) (A) is true but (R) is false . (D) (A) is false but (R) is true . 31. In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If ÐCBE = 65°, then what is the value of ÐDEC ? (A) 35° . (B) 55° . (C) 45° . (D) 25° . 32. Find the value of x in (A) 1 . x+2. x +2. B A . C E . x +2. D . 3 x = x .. (B) 3 . (C) 6 . (D) 12 . 33. If a clock strikes once at one O'clock, twice at two O'clock and twelve times at 12 O'clock and again once at one O'clock and so on, how many times will the clock strike in the course of 2 days? (A) 156 . (B) 312 . (C) 78 5 . (D) 288 3 rd IMO | LevelI | Class 10 .

(27) 3rd IMO - 2009. 34. The area of a square inscribed in a semicircle to the area of a square inscribed in a quadrant of the same circle is _______ (A) 2 : 1 . (B) 3 : 2 . (C) 5 : 3 . (D) 8 : 5 . 35. In a long jump contest, the average jump length of the successful competitors was 6.4 metres and that of the unsuccessful competitors was 4.4 metres. If the average jump length of all competitors was 4.8 metres, the percentage of successful competitors is ______ (A) 25% . (B) 20% . (C) 16% . (D) 4% . 36. The sum of the perpendicular distances from a point P inside a regular hexagon of side 10 cm to its sides is _______ (A) Depends on the position of P . (B) 30 3 cm . (C) 60 3 cm . (D) 45 3 cm . 37. When x 94 – 7x 19 + 5x 4 – x + K is divided by (x – 1), then the remainder is –1. The remainder obtained when it is divided by (x + 1), is _______ (A) 0 . (B) 15 . (C) –1 . (D) 10 . 38. In the given multiplication, a and b are natural numbers. Then (a + b) is _____ (A) 5 . (B) 6 . (C) 8 . (D) 9 . 3a ´ b2 70 140 1470 . 39. The number of pythagorean triplets (a, b, c) where a 2 + b 2 = c 2 and each a, b, c being odd is ___ (A) 3 . (B) 1 . (C) 0 . (D) Infinite . 40. When onefifth of the adults left a neighbourhood picnic, the ratio of adults to children was 2 : 3. Later, when 44 children left, the ratio of children to adults was 2 : 5. How many people remained at the picnic? (A) 56 . (B) 65 . (C) 85 . (D) 58 . SECTION III : EVERYDAY MATHEMATICS 41. I bought 10 pens, 14 pencils and 4 erasers. Ravi bought 12 pens, 8 erasers and 28 pencils for an amount which was half more than what I had paid. What percent of the total amount paid by me was paid for the pens? (A) 37.5% . (B) 62.5% . (C) 50% . (D) None of these . 42. On Ashok Marg three consecutive traffic lights change after 36, 42 and 72 seconds respectively. If the lights are first switched on at 9:00 A.M. sharp, at what time will they change simultaneously? (A) 9 : 08 : 04 . (B) 9 : 08 : 24 . (C) 9 : 08 : 44 . (D) None of these . 43. Ravi's monthly salary is A rupees. Of this, he spends X rupees. The next month he has an increment of C% in his salary and D% in his expenditure. The new amount saved is ______ C ö D ö æ æ (A) A ç 1 + ÷ - X ç 1 + ÷ è 100 ø è 100 ø. (C). D ö æ A ö æ (B) ç ÷ (C - D ) X ç 1 + ÷ è 100 ø è 100 ø. X (C - D ) 100 . 3 rd IMO | LevelI | Class 10 . (D). 6 . X. (C + D ) 100 .

(28) 3rd IMO - 2009. 44. A leap year started on Monday. The days appearing 53 times are _____ (A) Sunday and Monday . (B) Monday and Tuesday . (C) Tuesday and Wednesday . (D) Saturday and Sunday . 45. A thief steals a car at 1.30 p.m. and drives it at 40 km an hour. The theft is discovered at 2 p.m. and the owner sets off in another car at 50 km an hour. He will overtake the thief at ______ (A) 3:30 p.m. . (B) 4 p.m. . (C) 4:30 p.m. . (D) 6:30 p.m. . A ' s share B ' s share C ' s share 2 46. A sum of Rs. 1300 is divided between A, B, C and D such that B ' s share = C ' s share = D ' s share = 3 . Then, A's share is _____ . (A) Rs. 140 . (B) Rs. 160 . (C) Rs. 240 . (D) Rs. 320 . 47. The given diagram represents the area swept by the wiper of a car. With the dimensions given in the figure, calculate the shaded area swept by the wiper. O. . m 7 c. 30° . D . A . c 14 m . B . (A) 102.67 cm 2 . C . (B) 205.34 cm 2 . (C) 51.33 cm 2 . (D) 208.16 cm 2 . 48. A student is declared passed in the exam only if he/she clears at least two subjects. The number of students who were declared passed in this exam is ______ Maths 16 . 13 . 6 8 . Physics 22 . 12 . 19 Chemistry . (A) 33 . (B) 66 . (C) 39 . (D) 78 . 49. A circular swimming pool is surrounded by a concrete walk 4 m wide. If the area of the walk is . 11 25 . that of the pool, then the radius of the pool is _______ (A) 20 m . (B) 8 m . (C) 30 m . (D) 16 m . 50. In a box there are coins and rings which are either silver or gold. If 30% of the objects in the box are coins and 40% of the rings are silver, what percentage of the objects in the box are gold rings? (A) 60% . (B) 30% . (C) 42% 7 . (D) 70% 3 rd IMO | LevelI | Class 10 .

(29) 4th. Year 2010.

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